58. We note that, as result of the fact that the Coulomb force is inversely proportional to r 2 , a particle of charge Q which is distance d from the origin will exert a force on some charge q o at the origin of equal strength as a particle of charge 4 Q at distance 2 d would exert on q o . Therefore, q 6 = +8 e on the – y axis could be replaced with a +2 e closer to the origin (at half the distance); this would add to the q 5 = +2 e already there and produce +4 e below the origin which exactly cancels the force due to

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Unformatted text preview: q 2 = +4 e above the origin. Similarly, q 4 = +4 e to the far right could be replaced by a + e at half the distance, which would add to q 3 = + e already there to produce a +2 e at distance d to the right of the central charge q 7 . The horizontal force due to this +2 e is cancelled exactly by that of q 1 = +2 e on the x axis, so that the net force on q 7 is zero....
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